Wen Yuan

activity

20242026

collaborators

10 papers

math.AP2026

Sharp Truncated Difference Estimates for Nonlocal Nonconvex Functionals Defined by Superlevel Sets

Feng Dai, Dachun Yang, Wen Yuan +1

Let $N \in N$ and $p \in [1, \infty)$ . In this article, we consider a family ${Φ_{λ, p}^{γ}}_{λ \in (0, \infty)}$ of nonlocal nonconvex functionals with a real parameter $γ$ and est…

math.CA2026

Sharp Quantitative Matrix-Weighted Bounds for Fractional Integrals and Sobolev Inequalities

Dachun Yang, Wen Yuan, Mingdong Zhang

For $α \in (0, n)$ , $p \in (1, \frac{n}{α})$ , $q := \frac{n p}{n - α p}$ , and $W \in A_{p, q}$ , we obtain the following matrix-weighted boundedness of the fractional integral $I_{α}$ : for an…

math.CA2026

Sharp Matrix-Weighted Lower Bounds for Non-Degenerate Convolution Calderón--Zygmund Operators

Fan Bu, Dachun Yang, Wen Yuan

Let $T$ be a convolution Calderón--Zygmund operator satisfying Hytönen's non-degeneracy condition. We prove that, for every $p \in (1, \infty)$ and $m \geq 3$ , there exists a positive co…

math.FA2026

Local Matrix Muckenhoupt Weights and Quantitative Weighted Inequalities Achieving Global Best Known Exponents

Tuomas Hytönen, Dachun Yang, Wen Yuan +1

In this article, we give various real-variable properties of local Muckenhoupt matrix weights $W$ and establish the quantitative boundedness of several operators on local matrix-we…

math.FA2026

Weak-type characterizations of Sobolev and bounded variation spaces on metric measure spaces

Tuomas P. Hytönen, Dachun Yang, Wen Yuan +1

Given a complete doubling metric measure space $(X, ρ, μ)$ supporting a Poincaré inequality, we prove weak-type characterizations of the Sobolev space $W ˙^{1, p} (μ)$ and the spac…

math.CA2026

Real-Variable Characterizations and Their Applications of Anisotropic Besov Spaces with Matrix $A_{\infty}$ Weights

Fan Bu, Shuaijun Feng, Qingying Xue +2

Let $α \in R$ , $p \in (0, \infty)$ , and $q \in (0, \infty]$ . In this article, we develop a theory of matrix-weighted anisotropic Besov spaces associated with an expansive matrix $…

math.CA2026

Fractional Gagliardo--Nirenberg Inequalities: Pointwise Estimates,Sharp Asymptotics, and Optimal Target Spaces

Pingxu Hu, Yinqin Li, Dachun Yang +1

We establish two pointwise estimates for fractional difference operators, tracking explicitly the dependence of the constants on the smoothness index $s \in (0, 1)$ . Using these, with…

math.CA2026

Optimal Weak-Type Estimates and Their Applications of Lifted Rough Maximal Operators

Dachun Yang, Wen Yuan, Yirui Zhao

Let $n \in N \cap [2, \infty)$ and $Ω \in L^{1} (S^{n - 1})$ with $Ω \neq \equiv 0$ . In this article, we introduce a new family of lifted rough maximal operators $\{\mathcal{M}_…

math.FA2025

Besov--Triebel--Lizorkin-Type Spaces with Matrix $A_{\infty}$ Weights

Fan Bu, Tuomas Hytönen, Dachun Yang +1

Introduced by A. Volberg, matrix $A_{p, \infty}$ weights provide a suitable generalization of Muckenhoupt $A_{\infty}$ weights from the classical theory. In our previous work, we esta…

math.CA2024

Sharp Weighted Cohen--Dahmen--Daubechies--DeVore Inequality with Applications to (Weighted) Critical Sobolev Spaces, Gagliardo--Nirenberg Inequalities, and Muckenhoupt Weights

Yinqin Li, Dachun Yang, Wen Yuan +2

In this article, we establish a quantitative weighted variant of a far-reaching inequality obtained by A. Cohen, W. Dahmen, I. Daubechies, and R. DeVore in 2003, whose dependence o…

Sharp Truncated Difference Estimates for Nonlocal Nonconvex Functionals Defined by Superlevel Sets

Sharp Quantitative Matrix-Weighted Bounds for Fractional Integrals and Sobolev Inequalities

Sharp Matrix-Weighted Lower Bounds for Non-Degenerate Convolution Calderón--Zygmund Operators

Local Matrix Muckenhoupt Weights and Quantitative Weighted Inequalities Achieving Global Best Known Exponents

Weak-type characterizations of Sobolev and bounded variation spaces on metric measure spaces

Real-Variable Characterizations and Their Applications of Anisotropic Besov Spaces with Matrix A∞​ Weights

Fractional Gagliardo--Nirenberg Inequalities: Pointwise Estimates,Sharp Asymptotics, and Optimal Target Spaces

Optimal Weak-Type Estimates and Their Applications of Lifted Rough Maximal Operators

Besov--Triebel--Lizorkin-Type Spaces with Matrix A∞​ Weights

Sharp Weighted Cohen--Dahmen--Daubechies--DeVore Inequality with Applications to (Weighted) Critical Sobolev Spaces, Gagliardo--Nirenberg Inequalities, and Muckenhoupt Weights

Real-Variable Characterizations and Their Applications of Anisotropic Besov Spaces with Matrix $A_{\infty}$ Weights

Besov--Triebel--Lizorkin-Type Spaces with Matrix $A_{\infty}$ Weights